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International Conference on Information Technology and Nanotechnology (ITNT)

Calculation of the resonance fluorescence spectrum for the three-level system in stochastic Schroedinger equation approach

Andrei Pavelev, Vitalii Semin, Sergey I. Kharitonov

Published Sep 20, 2021• 0 citations
Publisher

Abstract

Calculation of spectral characteristics of small dimension quantum systems is important for quantum optics, because it gives the opportunity to bind theoretical approaches for the description of these systems and experimental data. In present work, we consider the obtaining of the autocorrelation function and the resonance fluorescence spectrum of the three-level system in stochastic Schroedinger equation approach for each individual transition and for the whole system. We provide also results of the numerical simulation for the Markovian dynamics of the system and the resonance fluorescence spectrum for the one of transitions.

DOI
10.1109/itnt52450.2021.9649365

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Calculation of spectral characteristics of small dimension quantum systems is important for quantum optics, because it gives the opportunity to bind theoretical approaches for the description of these systems and experimental data. In present work, we consider the obtaining of the autocorrelation function and the resonance fluorescence spectrum of the three-level system in stochastic Schroedinger equation approach for each individual transition and for the whole system. We provide also results of the numerical simulation for the Markovian dynamics of the system and the resonance fluorescence spectrum for the one of transitions.
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Abstract We theoretically study the resonance fluorescence spectra of the lambda (Λ), vee (V) and cascade (Ξ) type three-level configurations. It is shown that each system with two detuning frequencies can be modelled using the SU(3) symmetry group to derive a generalized optical Bloch equation. For each configuration, this equation is solved to calculate the two-time correlation function by invoking the quantum regression theorem. The incoherent part of the power spectra gives the characteristic multi-peak fluorescence profiles which are different for different configurations. We also discuss how the dressed-state structure of such system can explain the origin of quintuplet profile of the fluorescent spectrum.
Strong laser fields, when tuned on resonance to an atomic (molecular) transition, give rise to the well-known triplet of resonance fluorescence. The laser field is normally assumed to be strong and monochromatic, even though the spectrum of real lasers is never a \ensuremath{\delta} function. A standard way to treat laser fluctuations has been to assume a well-defined nominal frequency and a randomly fluctuating phase. Recently we introduced the generalized jump model (GJM) for correlated phase fluctuations, where correlated phase jumps are considered, leading to Markovian as well as non-Markovian stochastic behavior. In the GJM, each phase jump may be correlated to the previous jump, and the degree of correlation, the typical jump size, and the mean time between jumps are the three parameters defining the stochastic character of the laser field. In this paper we apply the GJM model to the case of resonance fluorescence from an atom excited by a stochastic field. The ``standard'' Mollow triplet is obtained in the monochromatic limit of small jumps, and several new predictions are made in the different limits of the stochastic parameters. In the small-jump limit, a new ``field effect'' is predicted. The spectral line shape and the triplet separation deviate from the Mollow predictions for a monochromatic field in a substantial way, giving rise to observable differences.In the highly correlated small-jump limit, which is approximated by the Kubo oscillator model, the previous results are corrected to include nonzero line shifts and extended to the case of non-Lorentzian line shapes. In all regions, even input fields of the same line shape (which would be considered identical in the one-parameter linewidth description) give rise to very different output spectra, justifying the more complete stochastic description. Effective relaxation constants ${\mathrm{\ensuremath{\Gamma}}}_{1}^{\mathrm{*}}$ and ${\mathrm{\ensuremath{\Gamma}}}_{2}^{\mathrm{*}}$ that simplify the description of the spectrum are calculated in all appropriate cases, and ${\mathrm{\ensuremath{\Gamma}}}_{1}^{\mathrm{*}}$ is found to equal the input laser linewidth. In addition to predicting the resonance fluorescence spectra, the present analysis provides a way to extract the stochastic parameters from the nonlinear measurement in those cases where the linear characterization of the input field cannot do it. The analytic work is fully supported by extensive numerical simulations.
We have studied the fluorescence spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes are equal to the two atomic transition frequencies, respectively. The Green's function formalism has been used to calculate the excitation spectrum of the system. An expression for the spectral function describing the excitation spectrum of the system has been derived in a closed form in the limit of high photon densities. Numerical computation of the expression for the spectral function indicates that at each transition frequency there may exist either one pair or two pairs or three pairs of sidebands, in addition to the central peak, depending upon the relative strength of the Rabi frequencies involved.